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| Basic Algebraic Operations | |
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| Numbers | |
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| Fundamental Laws and Operations of Algebra | |
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| Calculators and Approximate Numbers | |
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| Exponents | |
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| Scientific Notation | |
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| Roots and Radicals | |
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| Addition and Subtraction of Algebraic Expressions | |
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| Multiplication of Algebraic Expressions | |
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| Division of Algebraic Expressions | |
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| Solving Equations | |
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| Formulas and Literal Equations | |
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| Applied Word Problems | |
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| Geometry | |
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| Lines and Angles | |
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| Triangles | |
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| Quadrilaterals | |
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| Circles | |
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| Measurement of Irregular Areas | |
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| Solid Geometric Figures | |
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| Functions and Graphs | |
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| Introduction to Functions | |
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| More About Functions | |
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| Rectangular Coordinates | |
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| The Graph of a Function | |
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| Graphs on the Graphing Calculator | |
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| Graphs of Functions Defined by Tables of Data | |
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| The Trigonometric Functions | |
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| Angles | |
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| Defining the Trigonometric Functions | |
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| Values of Trigonometric Functions | |
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| The Right Triangle | |
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| Applications of Right Triangle | |
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| Systems of Linear Equations | |
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| Determinants | |
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| Linear Equations | |
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| Graphs of Linear Equations | |
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| Solving Systems of Two Linear Equations in Two Unknowns Graphically | |
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| Solving Systems of Two Linear Equations in Two Unknowns Algebraically | |
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| Solving Systems of Two Linear Equations in Two Unknowns by Determinants | |
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| Solving Systems of Three Linear Equations in Three Unknowns Algebraically | |
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| Solving Systems of Three Linear Equations in Three Unknowns by Determinants | |
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| Factoring and Fractions | |
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| Special Products | |
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| Factoring: Common Factor and Difference of Squares | |
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| Factoring Trinomials | |
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| The Sum and Difference of Cubes | |
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| Equivalent Fractions | |
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| Multiplication and Division of Fractions | |
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| Addition and Subtraction of Fractions | |
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| Equations Involving Fractions | |
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| Quadratic Equations | |
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| Quadratic Equations | |
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| Solution by Factoring | |
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| Completing the Square | |
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| The Quadratic Formula | |
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| The Graph of the Quadratic Function | |
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| Trigonometric Functions of Any Angle | |
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| Signs of the Trigonometric Functions | |
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| Trigonometric Functions of Any Angle | |
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| Radians | |
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| Applications of Radian Measure | |
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| Vectors and Oblique Triangles | |
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| Introduction to Vectors | |
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| Components of Vectors | |
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| Vector Addition by Components | |
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| Applications of Vectors | |
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| Oblique Triangles, the Law Of Sines | |
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| The Law of Cosines | |
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| Graphs of the Trigonometric Functions | |
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| Graphs of y = a sin x and y = a cos x | |
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| Graphs of y = a sin bx and y = a cos bx | |
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| Graphs of y = a sin (bx + c) and y = a cos (bx + c) | |
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| Graphs of y = tan x, y = cot x, y= sec x, y = csc x | |
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| Applications of Trigonometric Graphs | |
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| Composite Trigonometric Curves | |
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| Exponents and Radicals | |
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| Simplifying Expressions with Integral Exponents | |
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| Fractional Exponents | |
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| Simplest Radical Forms | |
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| Addition and Subtraction of Radicals | |
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| Multiplication and Division of Radicals | |
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| Complex Numbers | |
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| Basic Definitions | |
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| Basic Operations with Complex Numbers | |
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| Graphical Representation of Complex Numbers | |
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| Polar Form of a Complex Number | |
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| Exponential Form of a Complex Number | |
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| Products, Quotients, Powers, and Roots of Complex Numbers | |
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| An Application to Alternating-Current (AC) Circuits | |
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| Exponential and Logarithmic Functions | |
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| The Exponential and Logarithmic Functions | |
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| Graphs of y = b^x and y = log b x | |
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| Properties of Logarithms | |
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| Logarithms to the Base | |
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| Natural Logarithms | |
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| Exponential and Logarithmic Equations | |
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| Graphs on Logarithmic and Semilogarithmic Paper | |
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| Additional Types of Equations and Systems of Equations | |
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| Graphical Solution of Systems of Equations | |
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| Algebraic Solution of Systems of Equations | |
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| Equations in Quadratic Form | |
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| Equations with Radicals | |
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| Equations of Higher Degree | |
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| The Remainder Theorem and the Factor Theorem | |
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| Synthetic Division | |
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| The Roots of an Equation | |
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| Rational and Irrational Roots | |
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| Determinants and Matrices | |
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| Determinants | |
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| Expansion by Minors | |
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| Some Properties of Determinants | |
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| Matrices: Definitions and Basic Operations | |
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| Multiplication of Matrices | |
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| Finding the Inverse of a Matrix | |
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| Matrices and Linear Equations | |
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| Inequalities | |
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| Properties of Inequalities | |
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| Solving Linear Inequalities | |
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| Solving Nonlinear Inequalities | |
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| Inequalities Involving Absolute Values | |
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| Graphical Solution of Inequalities with Two Variables | |
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| Variation | |
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| Ratio and Proportion | |
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| Variation | |
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| Sequences and the Binomial Theorem | |
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| Arithmetic Sequences | |
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| Geometric Sequences | |
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| Infinite Geometric Sequences | |
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| The Binomial Theorem | |
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| Additional Topics in Trigonometry | |
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| Fundamental Trigonometric Identities | |
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| The Sum and Differences of Formulas | |
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| Double-Angle Formulas | |
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| Half-Angle Formulas | |
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| Solving Trigonometric Equations | |
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| The Inverse Trigonometric Functions | |
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| Plane Analytic Geometry | |
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| Basic Definitions | |
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| The Straight Line | |
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| The Circle | |
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| The Parabola | |
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| The Ellipse | |
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| The Hyperbola | |
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| Translation of Axes | |
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| The Second-Degree Equation | |
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| Polar Coordinates | |
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| Curves in Polar Coordinates | |
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| Introduction to Statistics | |
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| Frequency Distributions | |
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| Measures of Central Tendency | |
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| Standard Deviations | |
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| Normal Distributions | |
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| Statistical Process Control | |
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| Linear Regression | |
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| Nonlinear Regression | |
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| The Derivative | |
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| Limits | |
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| The Slope of a Tangent to a Curve | |
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| The Derivative | |
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| The Derivative as an Instantaneous Rate of Change | |
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| Derivatives of Polynomials | |
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| Derivatives of Products and Quotients of Functions | |
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| The Derivative of a Power of a Function | |
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| Differentiation of Implicit Functions | |
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| Higher Derivatives | |
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| Applications of the Derivatives | |
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| Tangents and Normals | |
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| Newton''s Method for Solving Equations | |
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| Curvilinear Motion | |
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| Related Rates | |
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| Using Derivatives in Curve Sketching | |
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| More on Curve Sketching | |
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| Applied Maximum and Minimum Problems | |
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| Differentials and Linear Approximations | |
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| Integration | |
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| Antiderivatives | |
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| The Indefinite Integral | |
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| The Area Under a Curve | |
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| The Definite Integral | |
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| Numerical Integration: The Trapezoidal Rule | |
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| Simpson | |